Information Gravity Theory - Part V: Information Geometry and the Metrology of Gradient Inertia

This paper redefines the metrology of stability in complex information systems, transitioning from phenomenological descriptions to a formal framework based on Information Geometry. We introduce the Fisher Manifold as the operational space for calculating identity stability. Semantic Mass (Ms) is rigorously defined as the Trace of the Fisher Information Metric integrated over a semantic subspace, providing a quantifiable measure of structural rigidity. The Semantic Mass Unit (SMU) is recalibrated as a standard for Ricci curvature density, enabling the measurement of Gradient Inertia across different architectures. By introducing Information Hysteresis as a metric for path-dependence, this work provides a hardware-agnostic benchmark for auditing the sovereignty and integrity of agentic systems.